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<div class="title">SelfAdjointEigenSolver.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008-2010 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2010 Jitse Niesen &lt;jitse@maths.leeds.ac.uk&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_SELFADJOINTEIGENSOLVER_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_SELFADJOINTEIGENSOLVER_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./Tridiagonalization.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">class </span>GeneralizedSelfAdjointEigenSolver;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160; </div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SolverType,<span class="keywordtype">int</span> Size,<span class="keywordtype">bool</span> IsComplex&gt; <span class="keyword">struct </span>direct_selfadjoint_eigenvalues;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; </div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> DiagType, <span class="keyword">typename</span> SubDiagType&gt;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> computeFromTridiagonal_impl(DiagType&amp; diag, SubDiagType&amp; subdiag, <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> maxIterations, <span class="keywordtype">bool</span> computeEigenvectors, MatrixType&amp; eivec);</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;}</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html">   78</a></span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">class </span><a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver</a></div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;{</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;      Size = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;      ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;      Options = MatrixType::Options,</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    };</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    </div>
<div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a846b7e7de3b117ffcf4226d04ecec77b">   91</a></span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a846b7e7de3b117ffcf4226d04ecec77b">Scalar</a>;</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a7c52c334cec08ff33425e4b3f5474eb8">   92</a></span>&#160;    <span class="keyword">typedef</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a7c52c334cec08ff33425e4b3f5474eb8">Index</a>; </div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    </div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar,Size,Size,ColMajor,MaxColsAtCompileTime,MaxColsAtCompileTime&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">EigenvectorsType</a>;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a346d14d83fcf669a85810209b758feae">  102</a></span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a346d14d83fcf669a85810209b758feae">RealScalar</a>;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    </div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    <span class="keyword">friend</span> <span class="keyword">struct </span>internal::direct_selfadjoint_eigenvalues&lt;<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver</a>,Size,<a class="code" href="structEigen_1_1NumTraits.html">NumTraits</a>&lt;<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a846b7e7de3b117ffcf4226d04ecec77b">Scalar</a>&gt;::IsComplex&gt;;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a0fc5528f6a59753d3003907f3a88548f">  111</a></span>&#160;    typedef typename internal::plain_col_type&lt;MatrixType, RealScalar&gt;::type <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a0fc5528f6a59753d3003907f3a88548f">RealVectorType</a>;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    typedef <a class="code" href="classEigen_1_1Tridiagonalization.html">Tridiagonalization</a>&lt;MatrixType&gt; <a class="code" href="classEigen_1_1Tridiagonalization.html">TridiagonalizationType</a>;</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    typedef typename <a class="code" href="classEigen_1_1Matrix.html">TridiagonalizationType::SubDiagonalType</a> <a class="code" href="classEigen_1_1Matrix.html">SubDiagonalType</a>;</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a57b9403646ff5ee26b86e3821c08e729">  126</a></span>&#160;    <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver</a>()</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        : m_eivec(),</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;          m_eivalues(),</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;          m_subdiag(),</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;          m_hcoeffs(),</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;          m_info(InvalidInput),</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;          m_isInitialized(false),</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;          m_eigenvectorsOk(false)</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    { }</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00149"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#ac7a97741f1db4b17f7a00211667db5e2">  149</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#ac7a97741f1db4b17f7a00211667db5e2">SelfAdjointEigenSolver</a>(<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a7c52c334cec08ff33425e4b3f5474eb8">Index</a> size)</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        : m_eivec(size, size),</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;          m_eivalues(size),</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;          m_subdiag(size &gt; 1 ? size - 1 : 1),</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;          m_hcoeffs(size &gt; 1 ? size - 1 : 1),</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;          m_isInitialized(false),</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;          m_eigenvectorsOk(false)</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    {}</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00175"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#af9cf17478ced5a7d5b8391bb10873fac">  175</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#af9cf17478ced5a7d5b8391bb10873fac">SelfAdjointEigenSolver</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix, <span class="keywordtype">int</span> options = <a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>)</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;      : m_eivec(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;        m_eivalues(matrix.cols()),</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;        m_subdiag(matrix.rows() &gt; 1 ? matrix.rows() - 1 : 1),</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        m_hcoeffs(matrix.cols() &gt; 1 ? matrix.cols() - 1 : 1),</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;        m_isInitialized(false),</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;        m_eigenvectorsOk(false)</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    {</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a62817de3e0cbf009a02c7ece6a0e3d64">compute</a>(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>(), options);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a62817de3e0cbf009a02c7ece6a0e3d64">  218</a></span>&#160;    <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver</a>&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a62817de3e0cbf009a02c7ece6a0e3d64">compute</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix, <span class="keywordtype">int</span> options = <a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    </div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver</a>&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#afe520161701f5f585bcc4cedb8657bd1">computeDirect</a>(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">int</span> options = <a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160; </div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver</a>&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a297893df7098c43278d385e4d4e23fe4">computeFromTridiagonal</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a0fc5528f6a59753d3003907f3a88548f">RealVectorType</a>&amp; diag, <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">SubDiagonalType</a>&amp; subdiag , <span class="keywordtype">int</span> options=<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>);</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160; </div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00279"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a837627aecb3ba7ed40a2e1bfa3806d08">  279</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">EigenvectorsType</a>&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a837627aecb3ba7ed40a2e1bfa3806d08">eigenvectors</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;SelfAdjointEigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;      eigen_assert(m_eigenvectorsOk &amp;&amp; <span class="stringliteral">&quot;The eigenvectors have not been computed together with the eigenvalues.&quot;</span>);</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;      <span class="keywordflow">return</span> m_eivec;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;    }</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160; </div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00302"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#aaf4ed4172a517a4b9f0ab222f629e261">  302</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a0fc5528f6a59753d3003907f3a88548f">RealVectorType</a>&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#aaf4ed4172a517a4b9f0ab222f629e261">eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;SelfAdjointEigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;      <span class="keywordflow">return</span> m_eivalues;</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    }</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160; </div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00326"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a86020f7dece7dc114c8696af5617c792">  326</a></span>&#160;    MatrixType <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a86020f7dece7dc114c8696af5617c792">operatorSqrt</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;SelfAdjointEigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;      eigen_assert(m_eigenvectorsOk &amp;&amp; <span class="stringliteral">&quot;The eigenvectors have not been computed together with the eigenvalues.&quot;</span>);</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;      <span class="keywordflow">return</span> m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;    }</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160; </div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00351"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a4b3ddd941804994eaeede8cb65698bfd">  351</a></span>&#160;    MatrixType <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a4b3ddd941804994eaeede8cb65698bfd">operatorInverseSqrt</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;SelfAdjointEigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;      eigen_assert(m_eigenvectorsOk &amp;&amp; <span class="stringliteral">&quot;The eigenvectors have not been computed together with the eigenvalues.&quot;</span>);</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;      <span class="keywordflow">return</span> m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    }</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160; </div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00363"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a61de3180668fc0439251d832ebfe6b27">  363</a></span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a61de3180668fc0439251d832ebfe6b27">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;SelfAdjointEigenSolver is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;      <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;    }</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160; </div>
<div class="line"><a name="l00374"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#aefe08bf9db5a3ff94a241c56fe6e2870">  374</a></span>&#160;    <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#aefe08bf9db5a3ff94a241c56fe6e2870">m_maxIterations</a> = 30;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160; </div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;    EIGEN_STATIC_ASSERT_NON_INTEGER(<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a846b7e7de3b117ffcf4226d04ecec77b">Scalar</a>)</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160; </div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    <a class="code" href="classEigen_1_1Matrix.html">EigenvectorsType</a> m_eivec;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;    <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a0fc5528f6a59753d3003907f3a88548f">RealVectorType</a> m_eivalues;</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;    <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">TridiagonalizationType::SubDiagonalType</a> m_subdiag;</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">TridiagonalizationType::CoeffVectorType</a> m_hcoeffs;</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;    <span class="keywordtype">bool</span> m_eigenvectorsOk;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;};</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160; </div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> StorageOrder,<span class="keyword">typename</span> RealScalar, <span class="keyword">typename</span> Scalar, <span class="keyword">typename</span> Index&gt;</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="keyword">static</span> <span class="keywordtype">void</span> tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> start, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>, Scalar* matrixQ, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n);</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;}</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160; </div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;SelfAdjointEigenSolver&lt;MatrixType&gt;&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a62817de3e0cbf009a02c7ece6a0e3d64">SelfAdjointEigenSolver&lt;MatrixType&gt;</a></div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a62817de3e0cbf009a02c7ece6a0e3d64">::compute</a>(<span class="keyword">const</span> EigenBase&lt;InputType&gt;&amp; a_matrix, <span class="keywordtype">int</span> options)</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;{</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  <span class="keyword">const</span> InputType &amp;matrix(a_matrix.derived());</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160; </div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>);</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;  eigen_assert(matrix.cols() == matrix.rows());</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  eigen_assert((options&amp;~(EigVecMask|GenEigMask))==0</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;          &amp;&amp; (options&amp;EigVecMask)!=EigVecMask</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;          &amp;&amp; <span class="stringliteral">&quot;invalid option parameter&quot;</span>);</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  <span class="keywordtype">bool</span> computeEigenvectors = (options&amp;<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>)==<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>;</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = matrix.cols();</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;  m_eivalues.resize(n,1);</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160; </div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;  <span class="keywordflow">if</span>(n==1)</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;  {</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    m_eivec = matrix;</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;    m_eivalues.coeffRef(0,0) = numext::real(m_eivec.coeff(0,0));</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    <span class="keywordflow">if</span>(computeEigenvectors)</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;      m_eivec.setOnes(n,n);</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;    m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;    m_eigenvectorsOk = computeEigenvectors;</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;  }</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160; </div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;  <span class="comment">// declare some aliases</span></div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  RealVectorType&amp; diag = m_eivalues;</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;  EigenvectorsType&amp; mat = m_eivec;</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160; </div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  <span class="comment">// map the matrix coefficients to [-1:1] to avoid over- and underflow.</span></div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  mat = matrix.template triangularView&lt;Lower&gt;();</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;  RealScalar scale = mat.cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  <span class="keywordflow">if</span>(numext::is_exactly_zero(scale)) scale = RealScalar(1);</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;  mat.template triangularView&lt;Lower&gt;() /= scale;</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;  m_subdiag.resize(n-1);</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;  m_hcoeffs.resize(n-1);</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;  internal::tridiagonalization_inplace(mat, diag, m_subdiag, m_hcoeffs, computeEigenvectors);</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160; </div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;  m_info = internal::computeFromTridiagonal_impl(diag, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;  </div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;  <span class="comment">// scale back the eigen values</span></div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;  m_eivalues *= scale;</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160; </div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;  m_eigenvectorsOk = computeEigenvectors;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;}</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160; </div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;SelfAdjointEigenSolver&lt;MatrixType&gt;&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a297893df7098c43278d385e4d4e23fe4">SelfAdjointEigenSolver&lt;MatrixType&gt;</a></div>
<div class="line"><a name="l00468"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#a297893df7098c43278d385e4d4e23fe4">  468</a></span>&#160;<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a297893df7098c43278d385e4d4e23fe4">::computeFromTridiagonal</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#a0fc5528f6a59753d3003907f3a88548f">RealVectorType</a>&amp; diag, <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">SubDiagonalType</a>&amp; subdiag , <span class="keywordtype">int</span> options)</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;{</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;  <span class="comment">//TODO : Add an option to scale the values beforehand</span></div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;  <span class="keywordtype">bool</span> computeEigenvectors = (options&amp;<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>)==<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>;</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160; </div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  m_eivalues = diag;</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;  m_subdiag = subdiag;</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  <span class="keywordflow">if</span> (computeEigenvectors)</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;  {</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;    m_eivec.<a class="code" href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">setIdentity</a>(diag.size(), diag.size());</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  }</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  m_info = internal::computeFromTridiagonal_impl(m_eivalues, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160; </div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;  m_eigenvectorsOk = computeEigenvectors;</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;}</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160; </div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> DiagType, <span class="keyword">typename</span> SubDiagType&gt;</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;<a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> computeFromTridiagonal_impl(DiagType&amp; diag, SubDiagType&amp; subdiag, <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> maxIterations, <span class="keywordtype">bool</span> computeEigenvectors, MatrixType&amp; eivec)</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;{</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> info;</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160; </div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = diag.size();</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a> = n-1;</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> start = 0;</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> iter = 0; <span class="comment">// total number of iterations</span></div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;  </div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> DiagType::RealScalar RealScalar;</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;  <span class="keyword">const</span> RealScalar considerAsZero = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  <span class="keyword">const</span> RealScalar precision_inv = RealScalar(1)/<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;RealScalar&gt;::epsilon</a>();</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  <span class="keywordflow">while</span> (<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>&gt;0)</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  {</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = start; i&lt;<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>; ++i) {</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;      <span class="keywordflow">if</span> (numext::abs(subdiag[i]) &lt; considerAsZero) {</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;        subdiag[i] = RealScalar(0);</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;      } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;        <span class="comment">// abs(subdiag[i]) &lt;= epsilon * sqrt(abs(diag[i]) + abs(diag[i+1]))</span></div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;        <span class="comment">// Scaled to prevent underflows.</span></div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;        <span class="keyword">const</span> RealScalar scaled_subdiag = precision_inv * subdiag[i];</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;        <span class="keywordflow">if</span> (scaled_subdiag * scaled_subdiag &lt;= (numext::abs(diag[i])+numext::abs(diag[i+1]))) {</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;          subdiag[i] = RealScalar(0);</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;        }</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;      }</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    }</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160; </div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;    <span class="comment">// find the largest unreduced block at the end of the matrix.</span></div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;    <span class="keywordflow">while</span> (<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>&gt;0 &amp;&amp; numext::is_exactly_zero(subdiag[<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a> - 1]))</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;    {</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;      <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>--;</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;    }</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>&lt;=0)</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160; </div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;    <span class="comment">// if we spent too many iterations, we give up</span></div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;    iter++;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;    <span class="keywordflow">if</span>(iter &gt; maxIterations * n) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160; </div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;    start = <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a> - 1;</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;    <span class="keywordflow">while</span> (start&gt;0 &amp;&amp; !numext::is_exactly_zero(subdiag[start - 1]))</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;      start--;</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160; </div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;    internal::tridiagonal_qr_step&lt;MatrixType::Flags&amp;RowMajorBit ? RowMajor : ColMajor&gt;(diag.data(), subdiag.data(), start, <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>, computeEigenvectors ? eivec.data() : (Scalar*)0, n);</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  }</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;  <span class="keywordflow">if</span> (iter &lt;= maxIterations * n)</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>;</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160; </div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;  <span class="comment">// Sort eigenvalues and corresponding vectors.</span></div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;  <span class="comment">// TODO make the sort optional ?</span></div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;  <span class="comment">// TODO use a better sort algorithm !!</span></div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  <span class="keywordflow">if</span> (info == <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>)</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;  {</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; n-1; ++i)</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;    {</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k;</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;      diag.segment(i,n-i).minCoeff(&amp;k);</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;      <span class="keywordflow">if</span> (k &gt; 0)</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;      {</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;        numext::swap(diag[i], diag[k+i]);</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;        <span class="keywordflow">if</span>(computeEigenvectors)</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;          eivec.col(i).swap(eivec.col(k+i));</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;      }</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;    }</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;  }</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;  <span class="keywordflow">return</span> info;</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;}</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;  </div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SolverType,<span class="keywordtype">int</span> Size,<span class="keywordtype">bool</span> IsComplex&gt; <span class="keyword">struct </span>direct_selfadjoint_eigenvalues</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;{</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> run(SolverType&amp; eig, <span class="keyword">const</span> <span class="keyword">typename</span> SolverType::MatrixType&amp; A, <span class="keywordtype">int</span> options)</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;  { eig.compute(A,options); }</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;};</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160; </div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SolverType&gt; <span class="keyword">struct </span>direct_selfadjoint_eigenvalues&lt;SolverType,3,false&gt;</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;{</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::MatrixType MatrixType;</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::RealVectorType VectorType;</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::Scalar Scalar;</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::EigenvectorsType EigenvectorsType;</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  </div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160; </div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> computeRoots(<span class="keyword">const</span> MatrixType&amp; m, VectorType&amp; roots)</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  {</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>)</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;    EIGEN_USING_STD(atan2)</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>)</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">sin</a>)</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;    <span class="keyword">const</span> Scalar s_inv3 = Scalar(1)/Scalar(3);</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;    <span class="keyword">const</span> Scalar s_sqrt3 = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(Scalar(3));</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160; </div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;    <span class="comment">// The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0.  The</span></div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;    <span class="comment">// eigenvalues are the roots to this equation, all guaranteed to be</span></div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;    <span class="comment">// real-valued, because the matrix is symmetric.</span></div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;    Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(1,0)*m(2,0)*m(2,1) - m(0,0)*m(2,1)*m(2,1) - m(1,1)*m(2,0)*m(2,0) - m(2,2)*m(1,0)*m(1,0);</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;    Scalar c1 = m(0,0)*m(1,1) - m(1,0)*m(1,0) + m(0,0)*m(2,2) - m(2,0)*m(2,0) + m(1,1)*m(2,2) - m(2,1)*m(2,1);</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;    Scalar c2 = m(0,0) + m(1,1) + m(2,2);</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160; </div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;    <span class="comment">// Construct the parameters used in classifying the roots of the equation</span></div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;    <span class="comment">// and in solving the equation for the roots in closed form.</span></div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;    Scalar c2_over_3 = c2*s_inv3;</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;    Scalar a_over_3 = (c2*c2_over_3 - c1)*s_inv3;</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;    a_over_3 = numext::maxi(a_over_3, Scalar(0));</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160; </div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;    Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160; </div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;    Scalar q = a_over_3*a_over_3*a_over_3 - half_b*half_b;</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;    q = numext::maxi(q, Scalar(0));</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160; </div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;    <span class="comment">// Compute the eigenvalues by solving for the roots of the polynomial.</span></div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;    Scalar rho = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(a_over_3);</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;    Scalar theta = atan2(<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(q),half_b)*s_inv3;  <span class="comment">// since sqrt(q) &gt; 0, atan2 is in [0, pi] and theta is in [0, pi/3]</span></div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;    Scalar cos_theta = <a class="code" href="namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">cos</a>(theta);</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;    Scalar sin_theta = <a class="code" href="namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">sin</a>(theta);</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;    <span class="comment">// roots are already sorted, since cos is monotonically decreasing on [0, pi]</span></div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;    roots(0) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta); <span class="comment">// == 2*rho*cos(theta+2pi/3)</span></div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;    roots(1) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta); <span class="comment">// == 2*rho*cos(theta+ pi/3)</span></div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;    roots(2) = c2_over_3 + Scalar(2)*rho*cos_theta;</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  }</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160; </div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> extract_kernel(MatrixType&amp; mat, Ref&lt;VectorType&gt; res, Ref&lt;VectorType&gt; representative)</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;  {</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>);</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>);</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i0;</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;    <span class="comment">// Find non-zero column i0 (by construction, there must exist a non zero coefficient on the diagonal):</span></div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;    mat.diagonal().cwiseAbs().maxCoeff(&amp;i0);</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;    <span class="comment">// mat.col(i0) is a good candidate for an orthogonal vector to the current eigenvector,</span></div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;    <span class="comment">// so let&#39;s save it:</span></div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;    representative = mat.col(i0);</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;    Scalar n0, n1;</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;    VectorType c0, c1;</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;    n0 = (c0 = representative.cross(mat.col((i0+1)%3))).squaredNorm();</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;    n1 = (c1 = representative.cross(mat.col((i0+2)%3))).squaredNorm();</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;    <span class="keywordflow">if</span>(n0&gt;n1) res = c0/<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(n0);</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;    <span class="keywordflow">else</span>      res = c1/<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(n1);</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160; </div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  }</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160; </div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> run(SolverType&amp; solver, <span class="keyword">const</span> MatrixType&amp; mat, <span class="keywordtype">int</span> options)</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;  {</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;    eigen_assert(mat.cols() == 3 &amp;&amp; mat.cols() == mat.rows());</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;    eigen_assert((options&amp;~(EigVecMask|GenEigMask))==0</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;            &amp;&amp; (options&amp;EigVecMask)!=EigVecMask</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;            &amp;&amp; <span class="stringliteral">&quot;invalid option parameter&quot;</span>);</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;    <span class="keywordtype">bool</span> computeEigenvectors = (options&amp;<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>)==<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>;</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;    </div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;    EigenvectorsType&amp; eivecs = solver.m_eivec;</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;    VectorType&amp; eivals = solver.m_eivalues;</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;  </div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;    <span class="comment">// Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.</span></div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;    Scalar shift = mat.trace() / Scalar(3);</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;    <span class="comment">// TODO Avoid this copy. Currently it is necessary to suppress bogus values when determining maxCoeff and for computing the eigenvectors later</span></div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;    MatrixType scaledMat = mat.template selfadjointView&lt;Lower&gt;();</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;    scaledMat.diagonal().array() -= shift;</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;    Scalar scale = scaledMat.cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;    <span class="keywordflow">if</span>(scale &gt; 0) scaledMat /= scale;   <span class="comment">// TODO for scale==0 we could save the remaining operations</span></div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160; </div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;    <span class="comment">// compute the eigenvalues</span></div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;    computeRoots(scaledMat,eivals);</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160; </div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;    <span class="comment">// compute the eigenvectors</span></div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;    <span class="keywordflow">if</span>(computeEigenvectors)</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;    {</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;      <span class="keywordflow">if</span>((eivals(2)-eivals(0))&lt;=<a class="code" href="structEigen_1_1NumTraits.html">Eigen::NumTraits&lt;Scalar&gt;::epsilon</a>())</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;      {</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;        <span class="comment">// All three eigenvalues are numerically the same</span></div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;        eivecs.setIdentity();</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;      }</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;      {</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;        MatrixType tmp;</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;        tmp = scaledMat;</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160; </div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;        <span class="comment">// Compute the eigenvector of the most distinct eigenvalue</span></div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;        Scalar d0 = eivals(2) - eivals(1);</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;        Scalar d1 = eivals(1) - eivals(0);</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k(0), l(2);</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;        <span class="keywordflow">if</span>(d0 &gt; d1)</div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;        {</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;          numext::swap(k,l);</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;          d0 = d1;</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;        }</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160; </div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;        <span class="comment">// Compute the eigenvector of index k</span></div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;        {</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;          tmp.diagonal().array () -= eivals(k);</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;          <span class="comment">// By construction, &#39;tmp&#39; is of rank 2, and its kernel corresponds to the respective eigenvector.</span></div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;          extract_kernel(tmp, eivecs.col(k), eivecs.col(l));</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;        }</div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160; </div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;        <span class="comment">// Compute eigenvector of index l</span></div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;        <span class="keywordflow">if</span>(d0&lt;=2*<a class="code" href="structEigen_1_1NumTraits.html">Eigen::NumTraits&lt;Scalar&gt;::epsilon</a>()*d1)</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;        {</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;          <span class="comment">// If d0 is too small, then the two other eigenvalues are numerically the same,</span></div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;          <span class="comment">// and thus we only have to ortho-normalize the near orthogonal vector we saved above.</span></div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;          eivecs.col(l) -= eivecs.col(k).dot(eivecs.col(l))*eivecs.col(l);</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;          eivecs.col(l).normalize();</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;        }</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;        {</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;          tmp = scaledMat;</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;          tmp.diagonal().array () -= eivals(l);</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160; </div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;          VectorType dummy;</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;          extract_kernel(tmp, eivecs.col(l), dummy);</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;        }</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160; </div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;        <span class="comment">// Compute last eigenvector from the other two</span></div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;        eivecs.col(1) = eivecs.col(2).cross(eivecs.col(0)).normalized();</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;      }</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;    }</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160; </div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;    <span class="comment">// Rescale back to the original size.</span></div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;    eivals *= scale;</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;    eivals.array() += shift;</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;    </div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;    solver.m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;    solver.m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;    solver.m_eigenvectorsOk = computeEigenvectors;</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;  }</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;};</div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160; </div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;<span class="comment">// 2x2 direct eigenvalues decomposition, code from Hauke Heibel</span></div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> SolverType&gt; </div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;<span class="keyword">struct </span>direct_selfadjoint_eigenvalues&lt;SolverType,2,false&gt;</div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;{</div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::MatrixType MatrixType;</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::RealVectorType VectorType;</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::Scalar Scalar;</div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> SolverType::EigenvectorsType EigenvectorsType;</div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;  </div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> computeRoots(<span class="keyword">const</span> MatrixType&amp; m, VectorType&amp; roots)</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;  {</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>);</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;    <span class="keyword">const</span> Scalar t0 = Scalar(0.5) * <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*numext::abs2(m(1,0)));</div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;    <span class="keyword">const</span> Scalar t1 = Scalar(0.5) * (m(0,0) + m(1,1));</div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;    roots(0) = t1 - t0;</div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;    roots(1) = t1 + t0;</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;  }</div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;  </div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;  EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> run(SolverType&amp; solver, <span class="keyword">const</span> MatrixType&amp; mat, <span class="keywordtype">int</span> options)</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;  {</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>);</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;    EIGEN_USING_STD(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>);</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;    </div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;    eigen_assert(mat.cols() == 2 &amp;&amp; mat.cols() == mat.rows());</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;    eigen_assert((options&amp;~(EigVecMask|GenEigMask))==0</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160;            &amp;&amp; (options&amp;EigVecMask)!=EigVecMask</div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;            &amp;&amp; <span class="stringliteral">&quot;invalid option parameter&quot;</span>);</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160;    <span class="keywordtype">bool</span> computeEigenvectors = (options&amp;<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>)==<a class="code" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">ComputeEigenvectors</a>;</div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;    </div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;    EigenvectorsType&amp; eivecs = solver.m_eivec;</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;    VectorType&amp; eivals = solver.m_eivalues;</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;  </div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;    <span class="comment">// Shift the matrix to the mean eigenvalue and map the matrix coefficients to [-1:1] to avoid over- and underflow.</span></div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;    Scalar shift = mat.trace() / Scalar(2);</div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;    MatrixType scaledMat = mat;</div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;    scaledMat.coeffRef(0,1) = mat.coeff(1,0);</div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;    scaledMat.diagonal().array() -= shift;</div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;    Scalar scale = scaledMat.cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;    <span class="keywordflow">if</span>(scale &gt; Scalar(0))</div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;      scaledMat /= scale;</div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160; </div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;    <span class="comment">// Compute the eigenvalues</span></div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;    computeRoots(scaledMat,eivals);</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160; </div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;    <span class="comment">// compute the eigen vectors</span></div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;    <span class="keywordflow">if</span>(computeEigenvectors)</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;    {</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;      <span class="keywordflow">if</span>((eivals(1)-eivals(0))&lt;=<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(eivals(1))*<a class="code" href="structEigen_1_1NumTraits.html">Eigen::NumTraits&lt;Scalar&gt;::epsilon</a>())</div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;      {</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;        eivecs.setIdentity();</div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;      }</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;      {</div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;        scaledMat.diagonal().array () -= eivals(1);</div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;        Scalar a2 = numext::abs2(scaledMat(0,0));</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;        Scalar c2 = numext::abs2(scaledMat(1,1));</div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;        Scalar b2 = numext::abs2(scaledMat(1,0));</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;        <span class="keywordflow">if</span>(a2&gt;c2)</div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;        {</div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;          eivecs.col(1) &lt;&lt; -scaledMat(1,0), scaledMat(0,0);</div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;          eivecs.col(1) /= <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(a2+b2);</div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;        }</div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;        {</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;          eivecs.col(1) &lt;&lt; -scaledMat(1,1), scaledMat(1,0);</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;          eivecs.col(1) /= <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(c2+b2);</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;        }</div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160; </div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160;        eivecs.col(0) &lt;&lt; eivecs.col(1).unitOrthogonal();</div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;      }</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;    }</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160; </div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;    <span class="comment">// Rescale back to the original size.</span></div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;    eivals *= scale;</div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;    eivals.array() += shift;</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160; </div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;    solver.m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;    solver.m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;    solver.m_eigenvectorsOk = computeEigenvectors;</div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;  }</div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;};</div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160; </div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;}</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160; </div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160;SelfAdjointEigenSolver&lt;MatrixType&gt;&amp; <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#afe520161701f5f585bcc4cedb8657bd1">SelfAdjointEigenSolver&lt;MatrixType&gt;</a></div>
<div class="line"><a name="l00824"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointEigenSolver.html#afe520161701f5f585bcc4cedb8657bd1">  824</a></span>&#160;<a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html#afe520161701f5f585bcc4cedb8657bd1">::computeDirect</a>(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">int</span> options)</div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;{</div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;  internal::direct_selfadjoint_eigenvalues&lt;SelfAdjointEigenSolver,Size,NumTraits&lt;Scalar&gt;::IsComplex&gt;::run(*<span class="keyword">this</span>,matrix,options);</div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160;}</div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160; </div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160; </div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;<span class="comment">// Francis implicit QR step.</span></div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> StorageOrder,<span class="keyword">typename</span> RealScalar, <span class="keyword">typename</span> Scalar, <span class="keyword">typename</span> Index&gt;</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;<span class="keyword">static</span> <span class="keywordtype">void</span> tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> start, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>, Scalar* matrixQ, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n)</div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;{</div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;  <span class="comment">// Wilkinson Shift.</span></div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;  RealScalar td = (diag[<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>-1] - diag[<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>])*RealScalar(0.5);</div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;  RealScalar e = subdiag[<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>-1];</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;  <span class="comment">// Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still</span></div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;  <span class="comment">// underflow thus leading to inf/NaN values when using the following commented code:</span></div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;  <span class="comment">//   RealScalar e2 = numext::abs2(subdiag[end-1]);</span></div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160;  <span class="comment">//   RealScalar mu = diag[end] - e2 / (td + (td&gt;0 ? 1 : -1) * sqrt(td*td + e2));</span></div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;  <span class="comment">// This explain the following, somewhat more complicated, version:</span></div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;  RealScalar mu = diag[<a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a>];</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160;  <span class="keywordflow">if</span>(numext::is_exactly_zero(td)) {</div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;    mu -= numext::abs(e);</div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!numext::is_exactly_zero(e)) {</div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;    <span class="keyword">const</span> RealScalar e2 = numext::abs2(e);</div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;    <span class="keyword">const</span> RealScalar h = numext::hypot(td,e);</div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;    <span class="keywordflow">if</span>(numext::is_exactly_zero(e2)) {</div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;      mu -= e / ((td + (td&gt;RealScalar(0) ? h : -h)) / e);</div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;      mu -= e2 / (td + (td&gt;RealScalar(0) ? h : -h)); </div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160;    }</div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;  }</div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160; </div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;  RealScalar x = diag[start] - mu;</div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160;  RealScalar z = subdiag[start];</div>
<div class="line"><a name="l00860"></a><span class="lineno">  860</span>&#160;  <span class="comment">// If z ever becomes zero, the Givens rotation will be the identity and</span></div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160;  <span class="comment">// z will stay zero for all future iterations.</span></div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = start; k &lt; <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a> &amp;&amp; !numext::is_exactly_zero(z); ++k)</div>
<div class="line"><a name="l00863"></a><span class="lineno">  863</span>&#160;  {</div>
<div class="line"><a name="l00864"></a><span class="lineno">  864</span>&#160;    JacobiRotation&lt;RealScalar&gt; rot;</div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;    rot.makeGivens(x, z);</div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160; </div>
<div class="line"><a name="l00867"></a><span class="lineno">  867</span>&#160;    <span class="comment">// do T = G&#39; T G</span></div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;    RealScalar sdk = rot.s() * diag[k] + rot.c() * subdiag[k];</div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;    RealScalar dkp1 = rot.s() * subdiag[k] + rot.c() * diag[k+1];</div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160; </div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160;    diag[k] = rot.c() * (rot.c() * diag[k] - rot.s() * subdiag[k]) - rot.s() * (rot.c() * subdiag[k] - rot.s() * diag[k+1]);</div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160;    diag[k+1] = rot.s() * sdk + rot.c() * dkp1;</div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160;    subdiag[k] = rot.c() * sdk - rot.s() * dkp1;</div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;    </div>
<div class="line"><a name="l00875"></a><span class="lineno">  875</span>&#160;    <span class="keywordflow">if</span> (k &gt; start)</div>
<div class="line"><a name="l00876"></a><span class="lineno">  876</span>&#160;      subdiag[k - 1] = rot.c() * subdiag[k-1] - rot.s() * z;</div>
<div class="line"><a name="l00877"></a><span class="lineno">  877</span>&#160; </div>
<div class="line"><a name="l00878"></a><span class="lineno">  878</span>&#160;    <span class="comment">// &quot;Chasing the bulge&quot; to return to triangular form.</span></div>
<div class="line"><a name="l00879"></a><span class="lineno">  879</span>&#160;    x = subdiag[k];</div>
<div class="line"><a name="l00880"></a><span class="lineno">  880</span>&#160;    <span class="keywordflow">if</span> (k &lt; <a class="code" href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">end</a> - 1)</div>
<div class="line"><a name="l00881"></a><span class="lineno">  881</span>&#160;    {</div>
<div class="line"><a name="l00882"></a><span class="lineno">  882</span>&#160;      z = -rot.s() * subdiag[k+1];</div>
<div class="line"><a name="l00883"></a><span class="lineno">  883</span>&#160;      subdiag[k + 1] = rot.c() * subdiag[k+1];</div>
<div class="line"><a name="l00884"></a><span class="lineno">  884</span>&#160;    }</div>
<div class="line"><a name="l00885"></a><span class="lineno">  885</span>&#160;    </div>
<div class="line"><a name="l00886"></a><span class="lineno">  886</span>&#160;    <span class="comment">// apply the givens rotation to the unit matrix Q = Q * G</span></div>
<div class="line"><a name="l00887"></a><span class="lineno">  887</span>&#160;    <span class="keywordflow">if</span> (matrixQ)</div>
<div class="line"><a name="l00888"></a><span class="lineno">  888</span>&#160;    {</div>
<div class="line"><a name="l00889"></a><span class="lineno">  889</span>&#160;      <span class="comment">// FIXME if StorageOrder == RowMajor this operation is not very efficient</span></div>
<div class="line"><a name="l00890"></a><span class="lineno">  890</span>&#160;      Map&lt;Matrix&lt;Scalar,Dynamic,Dynamic,StorageOrder&gt; &gt; q(matrixQ,n,n);</div>
<div class="line"><a name="l00891"></a><span class="lineno">  891</span>&#160;      q.applyOnTheRight(k,k+1,rot);</div>
<div class="line"><a name="l00892"></a><span class="lineno">  892</span>&#160;    }</div>
<div class="line"><a name="l00893"></a><span class="lineno">  893</span>&#160;  }</div>
<div class="line"><a name="l00894"></a><span class="lineno">  894</span>&#160;}</div>
<div class="line"><a name="l00895"></a><span class="lineno">  895</span>&#160; </div>
<div class="line"><a name="l00896"></a><span class="lineno">  896</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00897"></a><span class="lineno">  897</span>&#160; </div>
<div class="line"><a name="l00898"></a><span class="lineno">  898</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00899"></a><span class="lineno">  899</span>&#160; </div>
<div class="line"><a name="l00900"></a><span class="lineno">  900</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_SELFADJOINTEIGENSOLVER_H</span></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a18e969adfdf2db4ac44c47fbdc854683"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">Eigen::MatrixBase::setIdentity</a></div><div class="ttdeci">Derived &amp; setIdentity()</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:875</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix&lt; Scalar, Size, Size, ColMajor, MaxColsAtCompileTime, MaxColsAtCompileTime &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html">Eigen::SelfAdjointEigenSolver</a></div><div class="ttdoc">Computes eigenvalues and eigenvectors of selfadjoint matrices.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:79</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a0fc5528f6a59753d3003907f3a88548f"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a0fc5528f6a59753d3003907f3a88548f">Eigen::SelfAdjointEigenSolver::RealVectorType</a></div><div class="ttdeci">internal::plain_col_type&lt; MatrixType, RealScalar &gt;::type RealVectorType</div><div class="ttdoc">Type for vector of eigenvalues as returned by eigenvalues().</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:111</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a297893df7098c43278d385e4d4e23fe4"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a297893df7098c43278d385e4d4e23fe4">Eigen::SelfAdjointEigenSolver::computeFromTridiagonal</a></div><div class="ttdeci">SelfAdjointEigenSolver &amp; computeFromTridiagonal(const RealVectorType &amp;diag, const SubDiagonalType &amp;subdiag, int options=ComputeEigenvectors)</div><div class="ttdoc">Computes the eigen decomposition from a tridiagonal symmetric matrix.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:468</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a346d14d83fcf669a85810209b758feae"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a346d14d83fcf669a85810209b758feae">Eigen::SelfAdjointEigenSolver::RealScalar</a></div><div class="ttdeci">NumTraits&lt; Scalar &gt;::Real RealScalar</div><div class="ttdoc">Real scalar type for MatrixType_.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:102</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a4b3ddd941804994eaeede8cb65698bfd"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a4b3ddd941804994eaeede8cb65698bfd">Eigen::SelfAdjointEigenSolver::operatorInverseSqrt</a></div><div class="ttdeci">MatrixType operatorInverseSqrt() const</div><div class="ttdoc">Computes the inverse square root of the matrix.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:351</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a61de3180668fc0439251d832ebfe6b27"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a61de3180668fc0439251d832ebfe6b27">Eigen::SelfAdjointEigenSolver::info</a></div><div class="ttdeci">ComputationInfo info() const</div><div class="ttdoc">Reports whether previous computation was successful.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:363</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a62817de3e0cbf009a02c7ece6a0e3d64"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a62817de3e0cbf009a02c7ece6a0e3d64">Eigen::SelfAdjointEigenSolver::compute</a></div><div class="ttdeci">SelfAdjointEigenSolver &amp; compute(const EigenBase&lt; InputType &gt; &amp;matrix, int options=ComputeEigenvectors)</div><div class="ttdoc">Computes eigendecomposition of given matrix.</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a7c52c334cec08ff33425e4b3f5474eb8"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a7c52c334cec08ff33425e4b3f5474eb8">Eigen::SelfAdjointEigenSolver::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:92</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a837627aecb3ba7ed40a2e1bfa3806d08"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a837627aecb3ba7ed40a2e1bfa3806d08">Eigen::SelfAdjointEigenSolver::eigenvectors</a></div><div class="ttdeci">const EigenvectorsType &amp; eigenvectors() const</div><div class="ttdoc">Returns the eigenvectors of given matrix.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:279</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a846b7e7de3b117ffcf4226d04ecec77b"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a846b7e7de3b117ffcf4226d04ecec77b">Eigen::SelfAdjointEigenSolver::Scalar</a></div><div class="ttdeci">MatrixType::Scalar Scalar</div><div class="ttdoc">Scalar type for matrices of type MatrixType_.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:91</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_a86020f7dece7dc114c8696af5617c792"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#a86020f7dece7dc114c8696af5617c792">Eigen::SelfAdjointEigenSolver::operatorSqrt</a></div><div class="ttdeci">MatrixType operatorSqrt() const</div><div class="ttdoc">Computes the positive-definite square root of the matrix.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:326</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_aaf4ed4172a517a4b9f0ab222f629e261"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#aaf4ed4172a517a4b9f0ab222f629e261">Eigen::SelfAdjointEigenSolver::eigenvalues</a></div><div class="ttdeci">const RealVectorType &amp; eigenvalues() const</div><div class="ttdoc">Returns the eigenvalues of given matrix.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:302</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_ac7a97741f1db4b17f7a00211667db5e2"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#ac7a97741f1db4b17f7a00211667db5e2">Eigen::SelfAdjointEigenSolver::SelfAdjointEigenSolver</a></div><div class="ttdeci">SelfAdjointEigenSolver(Index size)</div><div class="ttdoc">Constructor, pre-allocates memory for dynamic-size matrices.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:149</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_aefe08bf9db5a3ff94a241c56fe6e2870"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#aefe08bf9db5a3ff94a241c56fe6e2870">Eigen::SelfAdjointEigenSolver::m_maxIterations</a></div><div class="ttdeci">static const int m_maxIterations</div><div class="ttdoc">Maximum number of iterations.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:374</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_af9cf17478ced5a7d5b8391bb10873fac"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#af9cf17478ced5a7d5b8391bb10873fac">Eigen::SelfAdjointEigenSolver::SelfAdjointEigenSolver</a></div><div class="ttdeci">SelfAdjointEigenSolver(const EigenBase&lt; InputType &gt; &amp;matrix, int options=ComputeEigenvectors)</div><div class="ttdoc">Constructor; computes eigendecomposition of given matrix.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:175</div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointEigenSolver_html_afe520161701f5f585bcc4cedb8657bd1"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html#afe520161701f5f585bcc4cedb8657bd1">Eigen::SelfAdjointEigenSolver::computeDirect</a></div><div class="ttdeci">SelfAdjointEigenSolver &amp; computeDirect(const MatrixType &amp;matrix, int options=ComputeEigenvectors)</div><div class="ttdoc">Computes eigendecomposition of given matrix using a closed-form algorithm.</div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:824</div></div>
<div class="ttc" id="aclassEigen_1_1Tridiagonalization_html"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html">Eigen::Tridiagonalization</a></div><div class="ttdoc">Tridiagonal decomposition of a selfadjoint matrix.</div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:67</div></div>
<div class="ttc" id="agroup__Core__Module_html_ga0e45b6b2adead7c6a29815b99f9f14dd"><div class="ttname"><a href="group__Core__Module.html#ga0e45b6b2adead7c6a29815b99f9f14dd">Eigen::placeholders::end</a></div><div class="ttdeci">static const lastp1_t end</div><div class="ttdef"><b>Definition:</b> IndexedViewHelper.h:183</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:442</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">Eigen::NoConvergence</a></div><div class="ttdeci">@ NoConvergence</div><div class="ttdef"><b>Definition:</b> Constants.h:448</div></div>
<div class="ttc" id="agroup__enums_html_ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4"><div class="ttname"><a href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a7f7d17fba3c9bb92158e346d5979d0f4">Eigen::ComputeEigenvectors</a></div><div class="ttdeci">@ ComputeEigenvectors</div><div class="ttdef"><b>Definition:</b> Constants.h:407</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ad01d50a42869218f1d54af13f71517a6"><div class="ttname"><a href="namespaceEigen.html#ad01d50a42869218f1d54af13f71517a6">Eigen::cos</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_cos_op&lt; typename Derived::Scalar &gt;, const Derived &gt; cos(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae6e8ad270ff41c088d7651567594f796"><div class="ttname"><a href="namespaceEigen.html#ae6e8ad270ff41c088d7651567594f796">Eigen::sin</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sin_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sin(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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